...those who had had the sturdiest legs a decade ago showed the least fall-off in thinking skills, even when the scientists controlled for such factors as fatty diets, high blood pressure and shaky blood-sugar control...a muscularly powerful twin now performed about 18 percent better on memory and other cognitive tests than her weaker sister...in the brain imaging of the identical twins, if one genetically identical twin had had sturdier legs than the other at the start of the study, she now displayed significantly more brain volume and fewer “empty spaces in the brain” than her weaker sister.

Keep in mind the 'this is only one study' caution. It involved only a single analysis of the brain health of middle-aged female twins. However, it is a plausible result, because it is known that exercise causes muscles to release brain growth factors, and sturdier muscles might be expected to release more.